>There isn’t a rule of economics that says better technology makes more, better jobs for horses. It sounds shockingly dumb to even say that out loud, but swap horses for humans and suddenly people think it sounds about right.

Yes there is actually: https://en.m.wikipedia.org/wiki/Okishio%27s_theorem

Eh, kind of, but maybe not.

It talks about rate of profit over the economy as a whole. It says nothing about the distribution of said profits. Its assumed that human labors are the ones also reaping some of those profits because they are doing labor, hence wages from those labors remain stable. If for some reason there was 0 labor available to you the same premise could hold true, the rate the AI is earning could remain stable, you're just shit out of luck.

It's highly unclear to me what will happen. Probably learning math will be more accessible. But it's unclear how many humans will be involved at the forefront of math research. For example you can imagine a situation where in some parts of math large communities work in a direction guided by a few "visionaries". This sort of thing will not really happen after the commodization of theorem provers. Like instead of an advisor telling a PhD student a problem, they can just plug it in. On the other hand, in some sense the advisor and the student will be equal in the fact that the only thing you will need to do is ask questions?(last part is also speculative)

>Probably learning math will be more accessible.

I'm not quite sure what you mean. Isn't math already pretty much the most accessible thing that could be imagined? I can't think of any story of someone in the past century who wanted to study math but was unable to, except for reasons prohibiting any sort of academic study whatsoever (e.g. girls in Taliban controlled areas).

I don't think research math is that accessible! Granted theoretically it's possible to just read papers and do research--and possibly it's theoretically as accessible as possible. In practice people learn better with teachers and access to experts at the research level. If this pans out, we can commoditize access to experts (or even experts).

But even in 1913 a brilliant mathematician from the middle of nowhere could access a world class mentor. I would assume that this is so much easier these days. What would stand in the way of a modern day math prodigy from getting accepted into a good program?

Or is it about making this more accessible to students who are "merely good" rather than brilliant?

yes I mean more accessible to the general public yes.

Some people imagine AI will soon be a bit like being able to go to a university professor's office hours to ask questions and get detailed expert advice on any part of the undergraduate curriculum you're struggling with.

Except it'll be available 24/7 and you won't have to pass exams, spend $$$$, attend full time, and live in dorms and be in your late teens or early 20s to get access.

And you'll have to fact check every answer to make sure it's not a "hallucination".

> Before compilers, people wrote machine code by hand. It would have been reasonable to think that compilers would reduce the demand for programmers, but the opposite happened.

That analogy occurred to me too. But I'm not sure what the corresponding higher-level domain is that mathematicians might have to migrate to - in the way that assembly programmers started using high level languages. Writing prompts for maths LLMs, or wrangling teams of them, is hardly going to be well paid enough to facilitate a decent life in this era of late capitalism, or even pay uni fees.

And even if there are such higher-level domains, its not certain that they are compatable with available human cognitive ability or limits.

Lots of maths grads currently go into tech/finance/lifescience/whatever. I'm a dev and I can see those fields being eaten alive by this stuff. I don't want my kid to end up as a 2030-equivalent of a fully qualified assembly language programmer.

> Besides, these things have a way of surprising us. Before compilers, people wrote machine code by hand. It would have been reasonable to think that compilers would reduce the demand for programmers, but the opposite happened.

I see this reasoning a lot but for me it kinda screams "correlation is not causation". As time passed and technology advanced it was simply more widely used, both on a consumer and business level. Very well may be that if we had to write machine code by hand we would need 10x more developers and a salary of $1kk/year would be average at best.

Do you really think if we get some AI agent that can write a wholly working application based on natural language specification that wouldn't significantly reduce the need for human devs?